Rav Safra quotes Rabbi Yehoshua as suggesting that the Torah’s use of ve-shinnantem as the expression used to command that parents teach their children Torah (see Devarim 6:7) should be understood to mean that Torah study should be divided into three parts, and a person should divide his years so that one third of the time is spent studying mikra, one third studying Mishna, and one third Gemara (underlying concepts and discussion of the Mishna). The Gemara objects to this suggestion, arguing that a person cannot possibly know how long he will live, and will not be able to divide up his time properly. In response the Gemara concludes that a person should divide up his days, rather than his years.
Rashi understands the suggestion of dividing days to mean that the days of the week should be devoted to different areas of study. Tosafot disagree, and rule that every day should be divided up. This appears to be the source for the Ge’onic tradition – one that appears in our prayer books to this day – that includes korbanot, a section of readings culled from the written Torah, the Mishna and the Gemara, whose focus is on the daily sacrifices. Traditionally, people rely on a different suggestion raised by Tosafot in the name of Rabbeinu Tam, that the standard Babylonian Talmud includes a mixture of mikra, Mishna and Gemara, and its study fulfills the requirement of dividing the days between these different areas of Torah study.
In his Likkutei Torah, Rav Shneur Zalman mi-Liadi suggests that the categories should be viewed more broadly, and that mikra refers not only to the written Torah, but also to the midrashim and commentaries written about it, while Mishna refers to the halakhic part of the Torah. This allows a person to keep a schedule of dividing Torah into three parts even as he develops intellectually and needs less time for “simpler” aspects of Torah study.